Density functional theory study of the structure and energetics of negatively charged oligopyrroles

Abstract

First-principles calculations are used to investigate the electronic properties of negatively charged n-pyrrole oligomers with n = 2–18. Chains of neutral oligomers are bent, whereas the negatively charged oligomers become almost planar due to accumulation of negative charge at the end monomers. Isomers of short oligomers (n < 6) display negative electron affinity although the corresponding anions are energetically stable. For longer oligomers with n ≥ 6, the electron affinity is small and positive, slowly increasing with oligopyrrole length. Doping of 12-pyrrole with lithium atoms shows that negative oxidation states are possible due to electron transfer from dopant to oligomer at locations close to dopant. These 12-pyrrole regions support extra negative charge and exhibit a local structural change from benzenoid to quinoid structure in the CC backbone conjugation. Comparison between neutral and doped polypyrrole (PPy) indicates that doped polymers displays a substantial depletion of the band gap energy and the appearance of dopant-based bands in the gap for a 50% per monomer doping level. It is predicted that Li-doped PPy is not metallic. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Full text

Page 1

Density Functional Theory Study of the
Structure and Energetics of Negatively
Charged Oligopyrroles
YAFEI DAI,1SUGATA CHOWDHURY,1ESTELA BLAISTEN-BAROJAS1,2
1Computational Materials Science Center, George Mason University, MS 6A2, Fairfaax, VA 22030
2Department of Computational and Data Sciences, George Mason University, MS 6A2, Fairfax, VA 22030
Received 6 December 2009; accepted 10 February 2010
Published online 29 June 2010 in Wiley Online Library (wileyonlinelibrary.com).
DOI 10.1002/qua.22659
ABSTRACT: First-principles calculations are used to investigate the electronic
properties of negatively charged n-pyrrole oligomers with n ¼ 2–18. Chains of neutral
oligomers are bent, whereas the negatively charged oligomers become almost planar
due to accumulation of negative charge at the end monomers. Isomers of short
oligomers (n < 6) display negative electron affinity although the corresponding anions
are energetically stable. For longer oligomers with n ? 6, the electron affinity is small
and positive, slowly increasing with oligopyrrole length. Doping of 12-pyrrole with
lithium atoms shows that negative oxidation states are possible due to electron transfer
from dopant to oligomer at locations close to dopant. These 12-pyrrole regions support
extra negative charge and exhibit a local structural change from benzenoid to quinoid
structure in the CAC backbone conjugation. Comparison between neutral and doped
polypyrrole (PPy) indicates that doped polymers displays a substantial depletion of the
band gap energy and the appearance of dopant-based bands in the gap for a 50% per
monomer doping level. It is predicted that Li-doped PPy is not metallic.
Periodicals, Inc. Int J Quantum Chem 111: 2295–2305, 2011
V
C2010 Wiley
Key words: oligopyrrole; polypyrrole; density functional theory; electron affinity;
n-doping conducting polymers
1. Introduction
S
ince the discovery of polypyrrole (PPy)
almost 50 years ago [1, 2], a myriad of publi-
cations are now available, more than 800 this past
year alone according to Web of Science. PPy is a
prototype conducting polymer [3] that displays
unique mechanical, optical, electrical, and biocom-
patible properties. However, much about the
physical properties and structural characteristics
of PPy are still not well understood, with data
that is often contradictory. With the advent of
nanomaterials, today PPy is used as a component
Correspondence to: E. Blaisten-Barojas; e-mail: blaisten@gmu.
edu
Contract grant sponsor: National Science Foundation.
Contract grant number: CHE0626111.
International Journal of Quantum Chemistry, Vol 111, 2295–2305 (2011)
V
C 2010 Wiley Periodicals, Inc.

Page 2

at the nanoscale in a variety of sensors, fibers,
and coated foams among other nanostructures [4,
5]. For example, when shaped as a conduit, PPy
has been proven effective for biomaterials modifi-
cation and regeneration of damaged nerves [6, 7].
Polymerization occurs either electrochemically or
chemically with dopant anions that remain em-
bedded into the polymeric matrix. This constitutes
the oxidized phase of PPy that displays conduc-
tion and possesses quinoid structure. Therefore,
most commonly oxidized PPy is a polycationic
conductor that synthesizes forming thin or thick
films. A wide variety of electronegative dopants
have been used, such as chloride ions, polysty-
rene sulfonate, molecular and polymeric anions,
buffer salts [8–10], and several biologically active
anions [7, 11]. Oxidation properties are crucial for
affinity binding of peptides for chloride-doped
PPy [12]. By reduction, the electrical conduction
property is lost and the structure of the conju-
gated chain becomes benzenoid. However, the
polymeric PPy matrix is difficult to be fully
reduced, it is not crystalline, and displays regions
of stacked chains [13]. Electrochemical switching
from oxidized to reduced phases of PPy produces
up to 30% change in the sample volume. This
actuation propertyis
muscles [9, 10].
Oxidation by electronegative dopants that gain
electrons from the polymer is equivalent to p-
doping and is feasible because of the low work
function of PPy. A different oxidation mechanism
occurs when electropositive dopants donate elec-
trons to the polymer (n-doping) turning PPy into
a polyanionic system. This oxidation mechanism
is difficult to realize by electrochemical means. In
fact, researchers assess that they did not obtain
stable doped systems when electropositive atoms
or molecules were used in the electrochemical
process [13]. The often accepted reason for n-dop-
ing not being favored is the low electron affinity
of PPy and its oligomers. Therefore, PPy negative
oxidation states have been elusive to experimen-
talists. The purpose of this article is the investiga-
tion of the electron affinity of Py oligomers and
determination of the changes in the polymer
backbone structure when oligopyrroles are doped
with lithium.
Over the years, a series of theoretical studies
have provided different predictions for oligopyr-
roles. For example, changes in the UV and visible
absorption spectra of neutral and cation oligopyr-
roles due to chlorine dopants have been put
forward within hybrid density functional theory
exploited forartificial
(DFT) and pseudopotentials [14]. This publication
provides an extensive bibliography on previous
electronic structure calculations. Contemporarily
to Ref. 14, we published [15] a careful study of
oligopyrroles electronic structure and structure
optimization in their reduced and multiply oxi-
dized phases with fluorine dopants within all-
electron DFT approach (B3PW91). Here, we apply
the same methodology as in our pervious study
[15] for investigation of the electron affinity, struc-
tural effects of doping with lithium, and changes
in the electronic structure of oligopyrroles and
PPy. A clear difference emerges by comparing the
new results of negative oxidation levels with
those previously obtained for positive oxidation
levels.
Electronic structure studies of negatively oxi-
dized PPy and oligopyrroles are scarce. Early
work was done with low-level electronic structure
calculations. The pioneer HF calculations with
STO-3G basis sets of Bredas et al. [16] of tetrapyr-
role (4-Py) with and without Na dopants (n-type)
demonstrated an almost complete electron trans-
fer between the doping atoms and pyrrole (Py)
rings. Although the small basis set was inad-
equatefor an accurate
description, this work predicted that the domi-
nant state for conduction was attained with two
doping Na atoms located adjacent to each other
on top of two contiguous Py rings (50% per
monomer doping level). This is referred in the lit-
erature as bipolaron. Very recent DFT studies of
lithium-doped polythiophene [17] reported posi-
tive energies of formation for 20–100% per mono-
mer doping levels. This prediction indicates the
need of supplying to the oligomer about 5 kcal/
mol for each pair of Li dopants to attain a doped
system, which suggests a negative electron affin-
ity of the oligothiophenes. Negative electron affin-
ities of oligopyrroles n-Py up to n ¼ 16 were
reported within a molecular fragment approach
[18], thus, predicting unfavorable negative oxida-
tion of oligopyrroles. In this article, we calculate
electron affinities of n-Py up to n ¼ 18 within our
more advanced first principles methodology.
Because calculation
requires basis sets with polarization and diffuse
functions, one double-f and two triple-f basis sets
are considered here. This article is organized as
follows. Section 2 describes the computational
details for obtaining the electronic structure.
Section 3 investigates the structure, energetics,
and vibrational analysis of neutral and anion
electronic structure
of electronaffinities
DAI, CHOWDHURY, AND BLAISTEN-BAROJAS
2296
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY DOI 10.1002/quaVOL. 111, NO. 10

Page 3

bipyrrole, tripyrrole, and tetrapyrrole possible iso-
mers. Additionally, the isomerization reactions in
3-Py and 4-Py anions from anti-gauche to syn-
gauche structures are discussed in this section.
Energetics and electron affinities of n-Py neutral
and anion oligomers with n ? 6 are reported in
Section 4. This section contains a study of the
charge distribution and structure and of lithium-
doped 12-Py. Based on periodic boundary condi-
tions (PBC), section 5 is dedicated to the study of
the band structure of pristine and n-doped PPy
by considering an infinite chain of a 4-Py motif
decorated with two Li atoms. Section 6 concludes
this article.
2. Methods
All-electron DFT within the Becke three-param-
eter hybrid approach [19] including local and
nonlocal correlation functionals as implemented
in Gaussian09 [20] is adopted throughout this
study. The choice of the correlation functional is
based on comparative results of Py structure
using a variety of functionals: B3PW91 [21, 22],
B3LYP [23, 24], B3BMK [25], and M06-HF [26].
Results closest to experiment [27] are obtained
with B3PW91 reproducing the experimental C2v
planar structure of neutral Py monomer. The
B3PW91 approach is then adopted, which addi-
tionally allow for comparison with our previous
studies [15]. In the study of doped n-Py oligom-
ers, where a considerable charge transfer takes
place, comparison between results within B3PW91
andfullexchange M06-HF
reported.
Structures of oligomers are optimized using tri-
ple valence basis sets 6-311G, 6-311þþG with dif-
fuse functions and double valence basis sets 6-
31þG (3d, 3p) with diffuse and polarization func-
tions for all atoms. Comparison between the opti-
mal calculated structure of neutral Py and experi-
ment [27] indicates that these three basis sets
yield comparable relative errors in the geometry:
0.38% with 6-311G, 0.42% with 6-311þþG, and
0.37% with 6-31þG (3d,3p). The Py monomer has
a strong dipole moment along the direction of the
NAH bond (Y-axis) of 1.89 D with the 6-311þþG
basis sets (1.85 D with 6-31þG (3d,3p)). The quad-
rupole matrix is diagonal in a set of axis where
the X-axis is perpendicular to the NAH bond and
contained in the plane of the molecule and the Z-
approaches is
axis is perpendicular to the molecular plane pass-
ing through the center of the Py ring. The quad-
rupole matrix in this set of axis is diagonal with
the XX, YY, ZZ matrix elements having values of
?27.26, ?24.11, ?34.97 DA˚using 6-311þþG and
?27.55, ?24.32, ?34.33 DA˚using 6-31þG (3d,3p).
These properties are in excellent agreement with
our previous results using the 6-311G basis set
without diffuse or polarization functions [15].
Geometry optimization for each n-Py oligomer
is attained by minimizing the molecular electronic
energy with respect to coordinates of all atoms in
3D using the Berny algorithm and redundant in-
ternal coordinates [28, 29]. Optimizations ensure
accuracies of 10?4for distances or angles and
10?8Hartrees for energies. For n-Py optimized
geometries, the vibrational analysis is routinely
performed to attest for the existence of a mini-
mum. For transition states (TS), the displacement
of atoms corresponding to the vibrational mode
associatedwith theimaginary
checked to ensure that the TS geometry is
attained. Furthermore, the intrinsic reaction coor-
dinate method allows us to assess that the TS con-
nects the two desired minima (two different iso-
mers) along the potential energy surface [30, 31].
Solvent effects are included for the small oligom-
ers with the polarized continuum model approach
[32].
In forthcoming sections, binding energies E are
reported with respect to the separated atoms
energies: ?13.7133 eV for H, ?1027.4931 eV for C,
and ?1481.9450 eV for N with the 6-311G;
?13.7156 eV for H, ?1027.5601 eV for C, and
?1482.0417
?13.6642 eV for H, ?1027.4197 eV for C, and
?1482.0417 eV for N with the 6-31þG (3d,3p)
basis sets.
The electron affinity EA is calculated as the dif-
ference between all-electron total energies:
frequencyis
eVforN withthe 6-311þþG;
EA ¼ EtotalðneutralÞ ? EtotalðanionÞ;
(1)
where Etotal(neutral) is the total energy of the opti-
mized neutral oligomer and Etotal(anion) is the
total energy of the optimized singly negative-
charged oligomer. Singly negative charged n-Py
oligomers are referred to as anions in the follow-
ing sections.
For PPy with PBC, the band structure is
referred to the Fermi energy EF. The value of EF
is obtained by solving a self consistent equation
that equates the number of electrons N to the sum
DFT STUDY OF NEGATIVELY CHARGED OLIGOPYRROLES
VOL. 111, NO. 10DOI 10.1002/qua INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
2297

Page 4

of electron occupation probabilities (Fermi func-
tions) of eigenstates composing the bands:
N ¼
X
nband
a¼1
X
nk
k¼1
2
1 þ e
ðEa;k?EFÞ
KBT
(2)
where nband¼ 16 is the number of bands consid-
ered in this work, nk¼ 81 is the number of k-
points in each band allowing up to 162 electrons
per band, KBis Boltzman’s constant, T ¼ 600 K is
a broadening temperature and N ¼ 2nknband. Val-
ues of these parameters ensure accuracy of 0.01
eV in the determination of EF.
3. Bipyrrole, Tripyrrole, and
Tetrapyrrole Anions
The geometrical structure of bipyrrole, as well
as that of longer oligomers, is modulated the most
by the monomer rotational degree of freedom
around the CAC bond joining contiguous mono-
mers. Neutral bipyrrole (2-Py) has four stable iso-
mers: two puckered structures anti-gauche and syn-
gauche, and two planar structures anti and syn [15,
33]. These four neutral isomers are stable irrespec-
tive of the basis sets used. The anti-gauche isomer
is the lowest in energy with a torsion angle
around 150?followed by the syn-gauche isomer
that lies a few hundredths eV above as reported in
Table I and has a torsion angle around 50?. The
cation 2-Pyþdisplays two planar isomers: anti
(C2h) and syn (C2v) and the transition between
them is not thermally possible [15]. Our calcula-
tions of the anion 2-Py?demonstrate that the neg-
atively charged molecule has also two possible
planar isomers: anti (C2h) and syn (C2v). The low-
est energy isomer of 2-Py?is the C2v structure,
whereas the C2hstructure is higher in energy as
seen from values of the binding energies given in
Table I. These electronic states are doublets, with
very low spin contamination. Quartets states are
several eVs less stable. With the triple-f basis sets
the TS from the C2visomer to the C2hisomer is
0.20 eV (0.26 eV with 6-31þG (3d, 3p)). This TS
corresponds to a torsion barrier separating the two
isomers. The high energy of this TS eliminates the
possibility of thermally induced isomerization.
Both anion isomers have electronic energies above
their neutral counterparts. Consequently, the elec-
tron affinity EA is negative, as occurs in molecular
anions where the extra electron is dipole-bound
[34]. Values of EAs are reported in Table II. Per-
forming one-point CCSD/6-31G* calculations of
the optimized geometries of neutral and anion iso-
mers confirms the above results; namely, the C2v
anion isomer is 0.13 eV more stable that the C2h
anion isomer and the EA is negative. Thus, we
predict that 2-Py?will not be observed experimen-
tally because if a fairly long lifetime of the anion is
required for performing the measurement, elec-
tron recombination with the surroundings will
occur before the measure takes place.
Combinations of anti-gauche with syn-gauche
orientations of monomers in tripyrrole (3-Py?)
TABLE I
Binding energies of n-Py and n-Py2stable isomers with n 5 2, 3, 4. Energies are referred to the separated
atoms energies given in Section 2.
Neutral E/n (eV)Anion E/n (eV)
N IsomerState6-311G6-311þþG6-31þG(3d, 3p)State 6-311G6-311þþG6-31þG(3d,3p)
2
:;
::
:;:
::;
:::
:;:;
:;;:
:;::
::;;
:::;
::::
C2,1A
C2,1A
C1,1A
C1,1A
C1,1A
C2,1A
C2,1A
C1,1A
C2,1A
C1,1A
C2,1A
?53.4209
?53.3599
?52.6129
?52.5636
?52.5673
?52.2097
?52.1968
?52.1922
?52.1793
?52.1784
?52.1582
?53.1300
?53.0954
?52.3189
?52.2946
?52.2735
?51.9145
?51.9007
?51.8974
?51.8844
?51.8827
?51.8630
?54.9775
?54.9399
?54.1434
?54.1304
?54.1167
?53.7274
?53.7040
?53.6994
?53.6851
?53.6837
?53.6733
C2h,2Ag
C2v,2A1
C1,2A
C1,2A
C1,2A
C1,2A
C1,2A
C1,2A
C1,2A
C1,2A
C1,2A
?52.6860
?52.6994
?52.3243
?52.3362
?52.3448
?51.0819
?51.0880
?51.0825
?51.0821
?51.0912
?51.0916
?52.9188
?52.9600
?52.1983
?52.2122
?52.2743
?51.8370
?51.8411
?51.8358
?51.8342
?51.8423
?51.9241
?54.6165
?54.6319
?53.9450
?53.9570
?54.0018
?53.6606
?53.6541
?53.6476
?53.6464
?53.6534
?53.6779
3
4
DAI, CHOWDHURY, AND BLAISTEN-BAROJAS
2298
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRYDOI 10.1002/quaVOL. 111, NO. 10

Page 5

and tetrapyrrole (4-Py?) give rise to three and six
isomers, respectively. The three neutral isomers of
3-Py are shown in Figure 1(a). The ground states
of these neutral isomers are singlet electronic
states. Binding energies are reported in Table I,
including comparison of results calculated with
the three basis sets considered in this study. The
vibrational analysis of isomers and their anion
counterpart yields positive frequencies, indicating
that the values reported in Table I correspond to
minima of the potential energy surface. The 3-Py
isomer of lowest energy, isomer I, has two 150?
torsion angles(157?
with
between monomer planes containing the NAH
bond. Isomer III is the highest energy 3-Py isomer
that has two 43?torsion angles between monomer
planes (39?with 6-31þG (3d, 3p)). The two tor-
sion angles in isomer II are 150?and 43?(157?,
39?with 6-31þG (3d, 3p)). Two TSs, TS1and TS2,
lie between these three isomers ground states at
0.11 eV and 0.17 eV (0.13, 0.15 eV using 6-31þG
(3d, 3p)). The first transition structure has the
third ring in isomer I rotated 90?while the second
transition structure has the third ring of isomer II
rotated 90?. Schematics of the potential energy
along the isomerization path are depicted in Fig-
6-31þG (3d, 3p))
ure 1(b). Solvent effects, assuming a relative
dielectric constant for water of 78.355, were con-
sidered. The overall effect of solvent is to stabilize
the isomers and destabilize the TSs as indicated
in parenthesis in Figure 1. Our transition energies
are very close to the reported values of torsion
barriers obtained by fixing the geometry of the
rings and only relaxing both torsion angle and
interring bond length [33, 35]. Geometry optimi-
zation of 3-Py?anion isomers yields almost pla-
nar structures in doublet states. Table I contains
the binding energies of the three anion isomers
corresponding to geometry-optimized structures.
Isomer III, with the three NAH bonds pointing in
the same side of the chain, is the most stable 3-
Py?. This anionic isomer has a marginal (almost
zero) electron affinity as shown in Table II. There-
fore,underfavorable
electron attachment to 3-Py isomer III may be
observed because of a dipole binding mechanism
[34]. However, the most stable neutral isomer I
would need to overcome a 0.17 eV (0.15 eV with
6-31þG (3d, 3p)) isomerization barrier to trans-
form into isomer III before an electron could be
attached. Therefore, this process might be feasible
at high temperatures only.
For tetrapyrrole, there are six isomers combin-
ing the anti and syn orientations of the NAH
bonds. For simplicity, these isomers are repre-
sented with up/down arrows. States and binding
energies are reported in Table I, which corre-
spond to a full geometry optimization of each iso-
mer and each anion. The vibrational analysis of
all isomers and their anions yield positive fre-
quencies indicating that energies reported corre-
spond to minima of the electron energy surface.
The 4-Py neutral isomer :;:; (torsion angles 150?,
151?, 150?with 6-311þþG and 156?, 157?, 156?
with 6-31þG (3d, 3p)) is the most stable and the
isomer :::: (41?, 33?, 41?with 6-311þþG and 35?,
30?, 35?with 6-31þG (3d, 3p)) is the least stable.
The other four neutral isomers are ordered in
increasing energy order as :;;: (149?, 31?, 149?
with 6-311þþG and 155?, 27?, 155?with 6-31þG
(3d, 3p)), :;:: (150?, 153?, 40?with 6-311þþG and
156?, 158?, 36?with 6-31þG (3d, 3p)), ::;; (41?,
152?, 41?with 6-311þþG and 36?, 157?, 36?with
6-31þG (3d, 3p)), and :::; (40?, 35?, 149?with 6-
311þþG and 36?, 31?, 156?with 6-31þG (3d, 3p)).
The most stable 4-Py?anion is the :::: isomer.
This is an almost planar molecule with torsion
angles 4?, 6?, 4?(3?, 4?, 3?with 6-31þG (3d, 3p)).
This isomer displays a marginal almost zero
circumstances,a weak
TABLE II
Electron affinity of n-Py oligomers calculated
from Eq. (1).
n Isomer
EA (eV)
6-311þþG 6-31þG (3d,3p)
2
:;
::
:;:
::;
:::
:;:;
:;;:
:;::
::;;
:::;
::::
?0.4224
?0.2708
?0.3618
?0.2472
0.0024
?0.3100
?0.2384
?0.2464
?0.2008
?0.1616
0.2444
0.0432
0.2396
0.3087
0.4634
0.5709
0.6475
?1.1758
?1.2034
?0.7944
?0.5739
?0.1620
?0.2672
?0.1996
?0.2072
?0.1548
?0.1212
?0.0032
0.0557
0.2482
0.3155
0.4642
0.5705
0.6500
3
4
6
8
9
12
15
18
For n > 4 the most isomer reported is the most stable in
which the -anti-syn- monomer orientation is repeated.
DFT STUDY OF NEGATIVELY CHARGED OLIGOPYRROLES
VOL. 111, NO. 10 DOI 10.1002/quaINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
2299